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DINOCRATES
L. Kaliambos (Natural Philosopher) November 27, 2014 APPLYING A COMBINATORY METHOD FOR THE DIMENSIONS OF HEPHAESTION TOMB IN AMPHIPOLIS I DISCOVERED THAT DINOCRATES USED NOT ONLY THE ASTRONOMICAL NUMBERS 7 AND 12 OF THE WALLS OF ALEXANDRIA BUT ALSO THE MYSTIC NUMBERS 3 AND 4 OF PYTHAGOREANS ALONG WITH ROOT OF THE GOLDEN SECTION (Φ'''0.5 ) OF PARTHENON AND OF GREAT PYRAMID FOR THE CONSTRUCTION OF THE SURROUNDING WALL. THIS PHOTO IS FROM THE INTERVIEW WITH THE TITLE " AMPHIPOLIS, ALEXANDRIA, AND GREAT PYRAMID" I GAVE TO THE AUTHOR OF THE SPIRITUAL THESSALY, Mrs DIMITRA BARDANI, THROUGH THE TV THESSALIA (GREECE).' '''DINOCRATES ALSO USED THE GOLDEN RATIO FOR THE LION, THE TWO CARYATIDS, AND THE TWO SPHINXES GIVEN BY'' ' (a +b)/a = a/b = Φ = (1 + 50.5) / 2 = 1.6180339887.. ' 'Dinocrates of Rhodes (last quarter of the 4th century BC) was a Greek architect and technical adviser for Alexander the Great. He is known for his plan for the city of Alexandria, the funeral monument for the divine hero Hephaestion and the reconstruction of the Temple of Artemis at Ephesus, as well as other works. Using a combinatory method for the two plans of Dinocrates like the perimeter P of the walls of the ancient Alexandria and for the dimensions of the Amphipolis tomb I discovered that the Amphipolis tomb is the significant funerary monument (as a miniature of ancient Alexandria) made by the architect Dinocrates for the divine hero “HEPHAESTION”. (See my TOMB OF HEPHAESTION IN AMPHIPOLISand PLAN OF AMPHIPOLIS TOMB). Moreover in both cases Dinocrates based on the sacred numbers 7, 12, and 3 determined the perimeter P of the walls of Alexandria and the dimensions of the conic pyramid in Amphipolis by using an ancient Egyptian algebra or a geometric algebra created by Greeks from the time of Plato. Also for the designing the lion, the two Caryatids, and the two sphinxes in the Hephaestion tomb Dinocrates used the so-called golden section of mathematics. ( See my GOLDEN SECTION IN AMPHIPOLIS LION, GOLDEN SECTION IN AMPHIPOLIS SPHINXES, and DISCOVERIES IN AMPHIPOLIS ). It is of interest to note that Dinocrates for the construction of the surrounding wall used correctly the constant π = 3.1416 given by ' 'π = 4/Φ'0.5' ' - 0.003 = 4/1.272 - 0.003 = 3.1416' This is an Egyptian formula for π based on the construction of the great pyramid (2560 BC). Today it is well known that the height of the great pyramid includes the Φ0.5 = (1.618)0.5 = 1.272. (See my RELATION OF Pi to Phi AND MYSTIC NUMBERS). In the same way Phidias based on the math of great pyramid formulated the heigt (H) of the theoretical pyramid in Parthenon as ''' '''H = α3 Φ 0.5/(3y)2 ' (See my PARTHENON MATH AND GREAT PYRAMID). ' Moreover Dinocrates for designing the two Caryatids and the two sphinxes was based on the golden section of Caryatids in Erechtheion and the golden rectangles in Parthenon. ' ' According to the History of Greek People ( Volume Δ, pages 109 and 208) Dinocrates was the architect of Alexandria ( 331 BC) and the expensive Pyre of Hephaestion having a base at the size of one stadion . On the other hand on the page 245 of the same Volume one reads that after the death of Alexander (323 BC) the expensive Pyre was canceled By Perdiccas and the army. To avoid this confusion for the dimensions of the Amphipolis tomb I used the combinatory method like that of the British architect Ventris ( who in 1952 deciphered the linear B) and I discovered that in Amphipolis the conic pyramid has a circular base with a diameter d of one stadion, which means that the cancelled Pyre was replaced by the tomb in Amphipolis. It is of interest to note that in the “Dinocrates-WIKIPEDIA” one reads that Dinocrates was the architect of Pyre in Babylon and of the Amphipolis tomb in northern Greece. Whereas in the “Hephaestion-WIKIPEDIA” we read: “ It is possible that the Pyre was not burnt, but that it was actually intended as a tomb or lasting memorial; if so, it is likely that it was never completed, as there are references to expensive, uncompleted projects at the time of Alexander's own death.” That is, according to the History of Greek People (Hellenistic period) and the writings of WIKIPEDIA Dinocrates using the secrets from the Amun Oracle planned the ancient Alexandria and the tomb for the divine hero HEPHAESTION in Amphipolis, which replaces the Pyre. So I discovered that the stadion of he base of the planned Pyre is just the diameter d = 1 stadion = 157.5 m ) of the base of the conic pyramid in Amphipolis.'' '' In by paper SECRETS OF AMPHIPOLIS AND ALEXANDRIA I discovered that both Alexandria and the Amphipolis tomb were planned by Dinocrates. So they have the same sacred numbers 7 and 12. According to the History of Greek People ( Volume Δ, pages 109 and 208 ) Alexander the Great in both cases of the foundation of Alexandria in Egypt and the Tomb of the divine hero Hephaestion consulted the Oracle of Amun (having all sacred numbers like 7, 12 and 3). In the case of the foundation of Alexandria the topographic conditions between the sea and the lake Mareotis led the architect Dinocrates for planning a preliminary design with a parallelogram by using also the sacred number 3, since (7X12)/3 gives the sacred number 28. Note that 28/7 represents the 4 lunar phases. Under this condition Dinocrates determined the axes x = 31.5 stadia and y = 10.5 stadia where x/y = 3, while the perimeter P of the walls P = 2x +2y = (7X12) = 84 stadia should include the sacred numbers 7 and 12. Then writing 2y = 2x/3 Dinocrates formulated the following formula 2x + 2x/3 = (7X12) or 6x +2x = 3(7X12) or 8x = 3(7X12) So he found x = 3(7X12)/8 = 31.5 stadia and y = 31.5/3 = 10.5 stadia Here we see that Dinocrates in Egypt used a simple algebra with linear equations. Ancient Egyptian algebra dealt mainly with linear equations. The Rhind Papyrus, also known as the Ahmes Papyrus, is an ancient Egyptian papyrus written c. 1650 BCE by Ahmes, who transcribed it from an earlier work that he dated to between 2000 and 1800 BCE. It is the most extensive ancient Egyptian mathematical document known to historians. The Rhind Papyrus contains problems where linear equations of the form x + ax = b and x + ax + bx = c are solved, where a, b, and c are known and x, which is referred to as "aha" or heap, is the unknown. On the other hand in case in which the Egyptian algebra was not known to Dinocrates, today it is well known that Greek mathematicians created a geometric algebra. It is sometimes alleged that the Greeks had no algebra, but this is inaccurate. By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them, and with this new form of algebra they were able to find solutions to equations by using a process that they invented, known as "the application of areas". It is only a part of geometric algebra and it is thoroughly covered in Euclid's Elements. In my paper CONFUSING KASTA TOMB AND GEOMETRY using the same combinatory method as that used by the British architect Ventris, (who in 1952 deciphered linear B ), I discovered that the Kasta hill includes the numbers 7 and 12 and the mathematical constant C/d = π =3.1416 , which is equal to the perimeter P of the surrounding wall. .Note that Alexander the Great after the death of Hephaestion (324 BC) should like to plan the monument of the divine hero HEPHAESTION having a base at the size of one stadion.In Amphipolis today we see that the base is a circular wall of d =1 stadion having a height ( h ) of about 3 meters and a width (w) which could be determined by the two concetric circles measured outside and inside the wall. Under a careful analysis of the height h and the width w of the surrounding wall havingn P = 3.1416 stadia, I discovered also that the volume v of the marbles of the surrounding wall having the height h and the width w include the number 3. Starting with the radius of the circular base, R2 = 158.4/2 = 79.2 m, measured outside the wall by the team of the Amphipolis excavation, and using the medium R = 1 stadion/2 = 157.5/2 = 78.75 m, I determined the R1 of the inner concentric circle of the surrounding wall as R1 = R-(R2-R) = 78.75 - 0.45 = 78.3 m Under such concentric circles of the surrounding wall and using the sacred number 3 in the ratio h/w = 3, I found the volume v of the marbles of the surrounding wall existing over the ground. It is about v = 1,172.1 cubic meters. Since one cubic stadion, 1 St3 = (157.5)3 = 3,906,984.3 cubic meters surprisingly I discovered that the ratio 1,172.1/3,906,984.3 gives 0.3/103 cubic stadia That is, both the h/w = 3 and the volume v = 0.3/103 include the same sacred number 3 = (7X12)/28 In other words using the same combinatory method as that of the architect Ventris I deciphered the following math used by Dinocrates in his preliminary design for determining the variables h and w responsible for the construction of the surrounding wall in the topography of the Kasta hill near Amphipolis, based on the sacred number 3. Thus we emphasize that Dinocrates in his preliminary design for the construction of the surrounding wall should write the following equations h/w = 3 and v = 0.3/103 = hw(2πR) = hw(3.1416) cubic stadia That is, h(h/3)(3.1416) = 0.3/103 Or h2 = (0.9/0.31416)(1/104) and h = (0.9/0.31416)0.5(1/100) = 0.017 stadia Or h = 0.017(157.5) = 2.7 m and w = 2.7/3 = 0.9 m Note that today the mean height of the wall including the part over the ground and the part under the ground (foundation) is about 3 m. Today for measuring the volume V of circular wall having the two concentric circles with R2 and R1 we use the well known formula as V = h(πR22 - πR12 ) = hπ(R2 -R1) (R2 +R1) Note that Dinocrates for calculating v, using the following practical formula got the same results as v = h(R2-R1) 2π( R2 +R1)/2 = hπ(R2-R1)(R2+R1) That is, V = v . Archaeologists have also made a number of important discoveries on the site since August 2014. Apart from the sheer size of the monument, which experts say bears the handprint of Dinocrates of Rhodes, the chief architect of Alexander the Great, archaeologists have so far unearthed two female statues of the Caryatid type in the antechamber, which support the entrance to the second compartment of the tomb. The height (a) of each Caryatid is a = 2.27 m. The Caryatids are on a pedestal of height b = 1.4 m , making the total height (a + b) = 3.67 m of the statues. After a careful analysis of such dimensions I discovered that Dinocrates used also the so-called golden ratio or golden section. In mathematics '''GOLDEN SECTION '''is the division of a line segment into extreme and mean ratio. This is obtained by dividing a line into two parts such that the square of the one part is equal to the product of the whole segment and the other part. An approximate value for the ratio of the longer part (a) to the shorter part (b) is 1.62. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b >0, ( a +b ) / a = a/b = φ = 1.61803398875... Where the Greek letter φ represents the number of the golden ratio Usually an approximate value of the ratio a/b is 1.62. That is,for the Caryatids we get (a + b)/a = a/b = (2.27 + 1.4) /2.27 = 2.27/1.4 =1.62 Note that detailed measurements should be made by the excavation team could give the number φ. For example writing b =1.402937 one could get (2.27+1.402937)/2.27 = 2.27/1.402937 = 1.618034 It appears that the Egyptians may have used both π and φ in the design of the Great Pyramids. The Greeks are thought by some to have based the design of the Parthenon on this proportion, but this is subject to some conjecture. Phidias (500 BC – 432 BC), a Greek sculptor and mathematician, studied φ and applied it to the design of sculptures for the Parthenon. Plato (circa 428 BC – 347 BC), in his views on natural science and cosmology presented in his “Timaeus,” considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos. In nature this golden section as a principle may be observed in the arrangements of leaves on a twig, petals on a flower and the arms of the starfish. The ancient Greeks considered a rectangle whose sides are in this ratio to be aesthetically the most pleasing of all rectangles and constructed their buildings on this principle. Such discoveries lead also to the conclusion that the Amphipolis tomb is the funeral monument constructed for the divine hero HEPHAESTION and it is just the miniature of ancient Alexandria having the secrets of the Amun Oracle used in the ancient astronomy. Moreover after my discovery that the circular base of the Hephaestion tomb has a diameter d of one Alexandrian stadion ( d = 157.5 m) one concludes that the Hephaestion conic pyramid is the only survived monument which gives us the unit of length used by Eratosthenes in ancient Alexandria for measuring the circumference of our Earth. Note that Aristarchus of Samos based on the measurements of Eratosthenes found that the Sun is greater than the Earth. So he developed the heliocentric system for the progress of astronomy and the fundamental physics which led to the discovery of the universal law of gravity. Unfortunately Einstein in his INVALID GENERALRELATIVITY tried to modify the well-established laws of Newton and Galileo and did much to retard the progress of fundamental physics. (See my Newton and Galileo reject Einstein). Category:Fundamental physics concepts